Pythagorean Thought Class
 |
Description
Book Introduction
- A word from MD
-
Think like a mathematicianThere are hidden rules in everything in the world.
To explain or understand this rule, mathematics is needed.
Clear choices and creative imagination also have answers in mathematics.
This book examines the thoughts of mathematicians from Pythagoras to Heo Jun, and introduces how to discover, analyze, and utilize the world through the thinking of mathematicians.
January 20, 2023. Natural Science PD Ahn Hyun-jae
“Quick thinking, clear choices, and creative imagination
“How do you do it?”
Mathematicians know the answer!
How to discover, analyze, and utilize the world like a mathematician!
We encounter mathematics countless times in our daily lives.
There are countless instances where we use it: when we buy things, when we calculate our game scores, when we water our plants, when we cook, when we calculate our car's gas mileage, when we calculate our departure time from home to go on a trip, and so on.
That's why mathematics has a huge impact on how we understand the world, perceive situations, and make decisions.
The more you know about math, the faster your brain works, the faster your decisions become, and the clearer your choices become.
How do we do this mathematical thinking?
This book covers 33 different mathematical ideas from ancient mathematicians such as Pythagoras, Euclid, Fermi, Gauss, Hilbert, and Heo Jun to modern mathematicians.
Among them, you can learn concepts and theories from elementary to advanced mathematics, such as one-to-one correspondence, fractions, functions, geometry, Fibonacci sequence, Fermi estimate, fractals, and Riemann hypothesis.
Pythagoras was an ancient mathematician and great philosopher.
He used mathematics to do philosophy, and taught many of his students that mathematics was essential for understanding life.
The number he spoke of was the pinnacle of 'knowledge that connects me to the world and allows me to discover a world I never knew existed.'
His ideas influenced many later mathematicians, including Plato and Euclid.
As a mathematician and thinker who clarified problems, he lived a life of restraint.
His disciples inherited his ideas and followed his teachings to view and think about the world through mathematics.
The author of this book is also a mathematician who has long preached the fun and importance of mathematics through lectures and books.
Having been fascinated by mathematics since childhood and having worked as a mathematician for many years, he is an expert at discovering problems, expanding his thinking, solving them logically, and imagining and utilizing them.
The mathematical ideas of Pythagoras, many mathematicians, and the author are all incorporated into this book.
If you find math difficult but want to read a math book, if you are a student who wants to learn difficult math concepts in an easy and fun way, if you are a working person who wants to logically resolve conflicts or problems encountered in society, or if you are an adult who wants to expand and clarify the complex thoughts of everyday life, I recommend you read this book.
《Pythagorean Thought Class》 will help readers live their lives more easily.
“How do you do it?”
Mathematicians know the answer!
How to discover, analyze, and utilize the world like a mathematician!
We encounter mathematics countless times in our daily lives.
There are countless instances where we use it: when we buy things, when we calculate our game scores, when we water our plants, when we cook, when we calculate our car's gas mileage, when we calculate our departure time from home to go on a trip, and so on.
That's why mathematics has a huge impact on how we understand the world, perceive situations, and make decisions.
The more you know about math, the faster your brain works, the faster your decisions become, and the clearer your choices become.
How do we do this mathematical thinking?
This book covers 33 different mathematical ideas from ancient mathematicians such as Pythagoras, Euclid, Fermi, Gauss, Hilbert, and Heo Jun to modern mathematicians.
Among them, you can learn concepts and theories from elementary to advanced mathematics, such as one-to-one correspondence, fractions, functions, geometry, Fibonacci sequence, Fermi estimate, fractals, and Riemann hypothesis.
Pythagoras was an ancient mathematician and great philosopher.
He used mathematics to do philosophy, and taught many of his students that mathematics was essential for understanding life.
The number he spoke of was the pinnacle of 'knowledge that connects me to the world and allows me to discover a world I never knew existed.'
His ideas influenced many later mathematicians, including Plato and Euclid.
As a mathematician and thinker who clarified problems, he lived a life of restraint.
His disciples inherited his ideas and followed his teachings to view and think about the world through mathematics.
The author of this book is also a mathematician who has long preached the fun and importance of mathematics through lectures and books.
Having been fascinated by mathematics since childhood and having worked as a mathematician for many years, he is an expert at discovering problems, expanding his thinking, solving them logically, and imagining and utilizing them.
The mathematical ideas of Pythagoras, many mathematicians, and the author are all incorporated into this book.
If you find math difficult but want to read a math book, if you are a student who wants to learn difficult math concepts in an easy and fun way, if you are a working person who wants to logically resolve conflicts or problems encountered in society, or if you are an adult who wants to expand and clarify the complex thoughts of everyday life, I recommend you read this book.
《Pythagorean Thought Class》 will help readers live their lives more easily.
- You can preview some of the book's contents.
Preview
index
Introduction - Why did Pythagoras call the world 'numbers'?
Chapter 1: Thinking about the problem, discovering the invisible
01.
A Problem-Based Perspective on the World - The Traveling Salesman Problem
02.
Sometimes guessing solves the problem - Fermi's estimate
03.
Knowing the old is the key to knowing the new - Ongoijishin
04.
The ability to turn 8 billion thoughts into 1 - reduction
05.
Beyond points, lines, and planes to n-dimensions - Extension
· Pythagorean Thought - A Bridge to the Invisible World
Chapter 2: Thinking about logic, analyzing everyday life
06.
How to categorize everyday life by problem - Symbols and classification
07.
Metaverse, also used by BTS - Bitmap and Wave
08.
The Thoughts of Genius Mathematician Heo Jun: Connection and Structure
09.
How to Think Logically Like Gauss - The String of Thought
· Pythagorean Thoughts - What the Enlightened One Needs
Chapter 3: Thinking, Imagining, and Questioning About Creativity
10.
Imagine seeing a car license plate - Baesu
11.
How Brightly Do Stars Shine? - The Inverse Square Law
12.
The hidden angle in the bottle cap - abbreviation
13.
Are Biorhythms Real? - Least Common Multiple
14.
The Secret of the 60-Year Cycle - Jinbeop
15.
Finding Hidden Commonalities in Problems - Arrays
16.
What if the repetitions were infinite? - Fractals
· Pythagorean Thought - How to Understand the World through Numbers
Chapter 4: Changing Your Thinking and Ideas About Invention
17.
Discovering Paired Ideas - One-to-One Correspondence
18.
The Great Number 0, the Invention of 'Nothing' - Numbers
19.
A Novel Way to Represent Multiplication - Multiplication
20.
Mathematical Thinking for Fairness - Fractions
21.
Euclid was right, and he was wrong - Geometry
22.
How to reduce the margin of error - Drawing
23.
Einstein's Love Equation - Topology
· Pythagorean Thoughts - Discovering Life-Changing Proverbs
Chapter 5: Thoughts on Studying: Expanding from the Basics
24.
A solid foundation is essential for success - mathematical skills
25.
Just knowing the concept is half the battle - computational ability
26.
The idea that math isn't difficult - abstraction
27.
The Surprising Way to Be Good at Math - Comprehension
28.
If you know one, you see ten - regularity
· Pythagoras, a man who studied philosophy through mathematics
Chapter 6: Thinking about Applications, Thinking Like a Mathematician
29.
The Prisoner's Dilemma and the Chicken Game - Applied Mathematics
30.
Why Lee Sedol Lost to AlphaGo - Monte Carlo Exploration
31.
An Easy Way to Predict Population - Exponential Functions
32.
Can a plane be filled perfectly? - Hilbert's problem
33.
The Unsolved Mystery of Mathematics: The Riemann Hypothesis
· Pythagorean Thought - A Life of Integration and Application
Going Out _ Essential Thoughts When Reading the World Through Water
Chapter 1: Thinking about the problem, discovering the invisible
01.
A Problem-Based Perspective on the World - The Traveling Salesman Problem
02.
Sometimes guessing solves the problem - Fermi's estimate
03.
Knowing the old is the key to knowing the new - Ongoijishin
04.
The ability to turn 8 billion thoughts into 1 - reduction
05.
Beyond points, lines, and planes to n-dimensions - Extension
· Pythagorean Thought - A Bridge to the Invisible World
Chapter 2: Thinking about logic, analyzing everyday life
06.
How to categorize everyday life by problem - Symbols and classification
07.
Metaverse, also used by BTS - Bitmap and Wave
08.
The Thoughts of Genius Mathematician Heo Jun: Connection and Structure
09.
How to Think Logically Like Gauss - The String of Thought
· Pythagorean Thoughts - What the Enlightened One Needs
Chapter 3: Thinking, Imagining, and Questioning About Creativity
10.
Imagine seeing a car license plate - Baesu
11.
How Brightly Do Stars Shine? - The Inverse Square Law
12.
The hidden angle in the bottle cap - abbreviation
13.
Are Biorhythms Real? - Least Common Multiple
14.
The Secret of the 60-Year Cycle - Jinbeop
15.
Finding Hidden Commonalities in Problems - Arrays
16.
What if the repetitions were infinite? - Fractals
· Pythagorean Thought - How to Understand the World through Numbers
Chapter 4: Changing Your Thinking and Ideas About Invention
17.
Discovering Paired Ideas - One-to-One Correspondence
18.
The Great Number 0, the Invention of 'Nothing' - Numbers
19.
A Novel Way to Represent Multiplication - Multiplication
20.
Mathematical Thinking for Fairness - Fractions
21.
Euclid was right, and he was wrong - Geometry
22.
How to reduce the margin of error - Drawing
23.
Einstein's Love Equation - Topology
· Pythagorean Thoughts - Discovering Life-Changing Proverbs
Chapter 5: Thoughts on Studying: Expanding from the Basics
24.
A solid foundation is essential for success - mathematical skills
25.
Just knowing the concept is half the battle - computational ability
26.
The idea that math isn't difficult - abstraction
27.
The Surprising Way to Be Good at Math - Comprehension
28.
If you know one, you see ten - regularity
· Pythagoras, a man who studied philosophy through mathematics
Chapter 6: Thinking about Applications, Thinking Like a Mathematician
29.
The Prisoner's Dilemma and the Chicken Game - Applied Mathematics
30.
Why Lee Sedol Lost to AlphaGo - Monte Carlo Exploration
31.
An Easy Way to Predict Population - Exponential Functions
32.
Can a plane be filled perfectly? - Hilbert's problem
33.
The Unsolved Mystery of Mathematics: The Riemann Hypothesis
· Pythagorean Thought - A Life of Integration and Application
Going Out _ Essential Thoughts When Reading the World Through Water
Detailed image
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Into the book
People usually think of 'mathematics' as a tool for solving problems.
However, mathematics is a 'tool for finding problems' rather than a 'tool for solving problems', and mathematicians are not 'problem solvers' but rather 'problem creators'.
That's why people jokingly call mathematicians 'problem children'.
--- p.17
People who are good at math are generally good at logically solving various problems they encounter in real life.
If someone claims, "I wasn't good at math in school, but I can solve problems around me logically," then they are someone who unconsciously has mathematical thinking in their head and can easily solve problems logically.
--- p.51
There were already people who did a mathematical classification of sounds long ago in ancient times.
That's right, Pythagoras.
He established a musical system to make it easier for people to play and listen to music, which is the eight-note scale known as the 'Pythagorean scale': 'do, re, mi, fa, sol, la, ti, do'.
Pythagoras valued music.
Like mathematics, I thought it could help people see the structure of nature, and purify their bodies and minds, keeping our bodies and souls in perfect condition.
Pythagoras pondered how to systematize music so that it could be judged rationally, and how to create instruments that would produce accurate sounds.
--- p.77
Professor Heo Jun's research on 'connection' and 'structure' has great significance in modern society, as many modern technologies are connected to communications, networks, and complex systems.
In particular, since the algorithms used in today's computer computing, artificial intelligence, and big data are all representative applications of combinatorics, it is predicted that Professor Heo Jun-i's research results will be greatly influenced.
Professor Heo Jun's research achievements are expected to have a significant ripple effect, as they are closely related to various fields such as information and communication technology, semiconductor design, transportation, logistics, and statistical physics.
--- p.91
Gauss's teacher gave his students difficult math problems to give himself a brief break.
It was an addition problem asking to add numbers from 1 to 100.
(…) Gauss realized that there was a certain rule hidden in the problem his teacher gave him.
In other words, unlike other students, I learned that if I add 1 and the last number, 100, I get 101, and if I add 2 and 99, I get 101, and if I add 3 and 98, I get 101.
If you add them like this, you get 50 101s in total, so Gauss gave a very simple answer: the sum of 1 to 100 is 50×101=5,050.
The problem was solved by utilizing the ‘symmetry of arithmetic sequences’, which is used when deriving a formula for finding the sum of any arithmetic sequence.
--- p.97
Studying math trains you to use your mind to think and understand, not just to solve problems and simply memorize them.
That is, we train our brains with math.
Even in school, we learn math in the form of brain training, and as we advance in grade, the math becomes increasingly filled with formulas using letters rather than numbers.
The mathematical format of developing logic using formulas is used across fields and can be applied effectively.
--- p.195
To improve memory and attention, Pythagoras' disciples are said to have recited the following mantra as soon as they opened their eyes in the morning:
'The first thing you should do as soon as you open your eyes is to think about the things you need to do today in order.'
And before going to sleep, he says he reflects on the day by reciting the following verse and then falls asleep.
'Don't close your eyes and go to sleep until you look back three times on what you did today.
What did I do right? What did I do wrong? And what didn't I finish?
However, mathematics is a 'tool for finding problems' rather than a 'tool for solving problems', and mathematicians are not 'problem solvers' but rather 'problem creators'.
That's why people jokingly call mathematicians 'problem children'.
--- p.17
People who are good at math are generally good at logically solving various problems they encounter in real life.
If someone claims, "I wasn't good at math in school, but I can solve problems around me logically," then they are someone who unconsciously has mathematical thinking in their head and can easily solve problems logically.
--- p.51
There were already people who did a mathematical classification of sounds long ago in ancient times.
That's right, Pythagoras.
He established a musical system to make it easier for people to play and listen to music, which is the eight-note scale known as the 'Pythagorean scale': 'do, re, mi, fa, sol, la, ti, do'.
Pythagoras valued music.
Like mathematics, I thought it could help people see the structure of nature, and purify their bodies and minds, keeping our bodies and souls in perfect condition.
Pythagoras pondered how to systematize music so that it could be judged rationally, and how to create instruments that would produce accurate sounds.
--- p.77
Professor Heo Jun's research on 'connection' and 'structure' has great significance in modern society, as many modern technologies are connected to communications, networks, and complex systems.
In particular, since the algorithms used in today's computer computing, artificial intelligence, and big data are all representative applications of combinatorics, it is predicted that Professor Heo Jun-i's research results will be greatly influenced.
Professor Heo Jun's research achievements are expected to have a significant ripple effect, as they are closely related to various fields such as information and communication technology, semiconductor design, transportation, logistics, and statistical physics.
--- p.91
Gauss's teacher gave his students difficult math problems to give himself a brief break.
It was an addition problem asking to add numbers from 1 to 100.
(…) Gauss realized that there was a certain rule hidden in the problem his teacher gave him.
In other words, unlike other students, I learned that if I add 1 and the last number, 100, I get 101, and if I add 2 and 99, I get 101, and if I add 3 and 98, I get 101.
If you add them like this, you get 50 101s in total, so Gauss gave a very simple answer: the sum of 1 to 100 is 50×101=5,050.
The problem was solved by utilizing the ‘symmetry of arithmetic sequences’, which is used when deriving a formula for finding the sum of any arithmetic sequence.
--- p.97
Studying math trains you to use your mind to think and understand, not just to solve problems and simply memorize them.
That is, we train our brains with math.
Even in school, we learn math in the form of brain training, and as we advance in grade, the math becomes increasingly filled with formulas using letters rather than numbers.
The mathematical format of developing logic using formulas is used across fields and can be applied effectively.
--- p.195
To improve memory and attention, Pythagoras' disciples are said to have recited the following mantra as soon as they opened their eyes in the morning:
'The first thing you should do as soon as you open your eyes is to think about the things you need to do today in order.'
And before going to sleep, he says he reflects on the day by reciting the following verse and then falls asleep.
'Don't close your eyes and go to sleep until you look back three times on what you did today.
What did I do right? What did I do wrong? And what didn't I finish?
--- p.251
Publisher's Review
The most useful idea to solve a problem
- “Teacher, people ask why they should learn math.”
- “Give him a coin.
“Because he has to get something out of mathematics.”
People who are good at math are generally good at logically solving various problems they encounter in real life.
If someone claims, "I wasn't good at math in school, but I can solve problems around me logically," then that person is already good at mathematical thinking without even realizing it.
People usually think of 'mathematics' as a tool for solving problems, but mathematics is closer to a 'tool for finding problems' rather than a 'tool for solving problems'.
The ancient mathematician Pythagoras also used mathematics to teach philosophy, and he considered mathematics to be the first subject his students should learn.
I thought that in a world made up of numbers, understanding and comprehending numbers was the way to understand the world.
The power of mathematics to discover and explain the rules of the world
Another reason to think mathematically is to develop the ability to see the world rationally.
There are some unchanging rules hidden in everything in the world that we take for granted.
We study mathematics to develop the ability to explain rules in a logical and rational way.
For example, it is like the process of finding answers to the questions below.
'How many chickens are sold per day in our country?'
Curiosity about this can be both informative for those who want to do business and entertaining for those who simply want to gain knowledge by calculating numbers.
This type of calculation can be done with the 'Fermi Estimation', and can be done infinitely by replacing it with not only chicken but also coffee, hamburgers, etc.
Fermi, a mathematics professor at the University of Chicago, posed the question, “How many piano tuners live in Chicago?” to develop students’ thinking skills. When the students could not answer the question, he made five assumptions, made calculations, and came up with a guess.
It was an efficient way to obtain approximate values in a short period of time using basic knowledge and logical reasoning, and was close to the actual value.
The Fermi estimate can be used to calculate many values, such as the number of chickens sold, the number of hair salons, and the number of people attending a meeting, and more recently, it has been applied to difficult-to-count numbers, such as how many alien civilizations there are in our galaxy.
As such, this book is full of logical and interesting stories.
Pythagoras and the mathematicians who read the world through numbers
When Pythagoras was asked by his disciple, “What is a friend?”, he replied, “A friend is another ‘me.’
“Just like 220 and 284,” he replied.
When Einstein was asked by a student, “Can the love between people be expressed in an equation?”, he created the equation Love = 2□ + 2△ + 2● + 2V +8〈.
Professor Heo Jun-i, a Korean-American, studied 'combinatorial algebraic geometry' and won the Fields Medal by proving 11 difficult problems before he turned 40.
His research is expected to influence the development of IT and artificial intelligence for the next 100 years.
The 23 problems posed by Hilbert, the German mathematician who led modern mathematics, have influenced the development of modern science.
In 『Pythagorean Thought Class』, there are stories of many mathematicians who have seen the world through numbers and solved many problems.
They told an entertaining story about how they discovered, analyzed, and exploited the problem.
By looking into the mathematicians and their ideas, who have had a significant impact on the advancement of humanity from ancient times to the present, we can also broaden our perspective on the world.
A thread of thought for a better life
The author of this book is a mathematician who teaches mathematics at a university and has already written several mathematics books.
While writing this book, he said, "I wanted to share my thoughts on mathematical thinking because it can be very helpful in our lives."
Because mathematics is a tool that expands our thinking and helps us understand the world.
And the author emphasized the 'string of thought'.
In mathematics, it is important to learn one thing and then connect it to the rest.
As you read, you will discover the threads that tie complex thoughts together through various theories and discover ways to organize your thoughts into a coherent framework.
The more you read, the more interesting it will be to see how mathematicians solve various real-life problems rationally and logically.
For those who have difficulty approaching mathematics, it is explained using examples from everyday life and in easy language.
I hope that beginners who want to learn mathematics or those who want to learn how to think mathematically will find this book a meaningful read.
- “Teacher, people ask why they should learn math.”
- “Give him a coin.
“Because he has to get something out of mathematics.”
People who are good at math are generally good at logically solving various problems they encounter in real life.
If someone claims, "I wasn't good at math in school, but I can solve problems around me logically," then that person is already good at mathematical thinking without even realizing it.
People usually think of 'mathematics' as a tool for solving problems, but mathematics is closer to a 'tool for finding problems' rather than a 'tool for solving problems'.
The ancient mathematician Pythagoras also used mathematics to teach philosophy, and he considered mathematics to be the first subject his students should learn.
I thought that in a world made up of numbers, understanding and comprehending numbers was the way to understand the world.
The power of mathematics to discover and explain the rules of the world
Another reason to think mathematically is to develop the ability to see the world rationally.
There are some unchanging rules hidden in everything in the world that we take for granted.
We study mathematics to develop the ability to explain rules in a logical and rational way.
For example, it is like the process of finding answers to the questions below.
'How many chickens are sold per day in our country?'
Curiosity about this can be both informative for those who want to do business and entertaining for those who simply want to gain knowledge by calculating numbers.
This type of calculation can be done with the 'Fermi Estimation', and can be done infinitely by replacing it with not only chicken but also coffee, hamburgers, etc.
Fermi, a mathematics professor at the University of Chicago, posed the question, “How many piano tuners live in Chicago?” to develop students’ thinking skills. When the students could not answer the question, he made five assumptions, made calculations, and came up with a guess.
It was an efficient way to obtain approximate values in a short period of time using basic knowledge and logical reasoning, and was close to the actual value.
The Fermi estimate can be used to calculate many values, such as the number of chickens sold, the number of hair salons, and the number of people attending a meeting, and more recently, it has been applied to difficult-to-count numbers, such as how many alien civilizations there are in our galaxy.
As such, this book is full of logical and interesting stories.
Pythagoras and the mathematicians who read the world through numbers
When Pythagoras was asked by his disciple, “What is a friend?”, he replied, “A friend is another ‘me.’
“Just like 220 and 284,” he replied.
When Einstein was asked by a student, “Can the love between people be expressed in an equation?”, he created the equation Love = 2□ + 2△ + 2● + 2V +8〈.
Professor Heo Jun-i, a Korean-American, studied 'combinatorial algebraic geometry' and won the Fields Medal by proving 11 difficult problems before he turned 40.
His research is expected to influence the development of IT and artificial intelligence for the next 100 years.
The 23 problems posed by Hilbert, the German mathematician who led modern mathematics, have influenced the development of modern science.
In 『Pythagorean Thought Class』, there are stories of many mathematicians who have seen the world through numbers and solved many problems.
They told an entertaining story about how they discovered, analyzed, and exploited the problem.
By looking into the mathematicians and their ideas, who have had a significant impact on the advancement of humanity from ancient times to the present, we can also broaden our perspective on the world.
A thread of thought for a better life
The author of this book is a mathematician who teaches mathematics at a university and has already written several mathematics books.
While writing this book, he said, "I wanted to share my thoughts on mathematical thinking because it can be very helpful in our lives."
Because mathematics is a tool that expands our thinking and helps us understand the world.
And the author emphasized the 'string of thought'.
In mathematics, it is important to learn one thing and then connect it to the rest.
As you read, you will discover the threads that tie complex thoughts together through various theories and discover ways to organize your thoughts into a coherent framework.
The more you read, the more interesting it will be to see how mathematicians solve various real-life problems rationally and logically.
For those who have difficulty approaching mathematics, it is explained using examples from everyday life and in easy language.
I hope that beginners who want to learn mathematics or those who want to learn how to think mathematically will find this book a meaningful read.
GOODS SPECIFICS
- Date of issue: January 17, 2023
- Page count, weight, size: 344 pages | 520g | 140*210*20mm
- ISBN13: 9791191104578
- ISBN10: 1191104575
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